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Multiplication of a Vector by a Scalar

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Question

If $¯ a$ and $¯ b$ are non-collinear unit vectors and $| ¯ a + ¯ b | = \sqrt{3}$ then $(2 ¯ a + 5 ¯ b) \cdot (3 ¯ a - ¯ b) = ?$

A

\frac{15}{4}

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B

\frac{15}{2}

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C

15

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D

16

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Solution

The correct option is D $\frac{15}{2}$

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Similar questions

¯ a

¯ b

are non-collinear unit vectors and

∣ ∣ ¯ a + ¯ b ∣ ∣ = \sqrt{3}

(2 ¯ a + 5 ¯ b) \cdot (3 ¯ a - ¯ b) = ?

¯ a, ¯ b, ¯ c

are non-coplaner vectors, then prove that the vectors

3 ¯ a + ¯ b + ¯ c, 2 ¯ a + 2 ¯ b + 3 ¯ c, ¯ a + 3 ¯ b + 5 ¯ c

¯ a

¯ b

are non collinear vectors. If

¯ c = (x - 2) ¯ a + ¯ b

¯ d = (2 x + 1) ¯ a - ¯ b

are collinear vectors, then find the value of

x

¯ a

¯ b

are units vectors and

¯ c

2 (¯ a \times ¯ b) + ¯ c = ¯ b \times ¯ c

then the maximum value of

∣ ∣ (¯ a \times ¯ c) . ¯ b ∣ ∣

¯ a, ¯ b, ¯ c

are three non-zero vectors no two of which are collinear and the vector

¯ a + ¯ b

is collinear with

¯ c

¯ b + ¯ c

is collinear with

¯ a

¯ a + ¯ b + ¯ c

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